# How do you write these numbers from least to greatest: 0.63, 0.6, 0.633, 0.603, 0.06?

Mar 5, 2018

$0.06 < 0.6 < 0.603 < 0.63 < 0.633$

#### Explanation:

Lets write fully every number:

$0.06 = 0.06000$
$0.6 = 0.6000$
$0.603 = 0.6030$
$0.63 = 0.6300$
$0.633 = 0.6330$

It's like thousands, only in decimal places, if that makes sense to you.

So there you go:

$0.06 < 0.6 < 0.603 < 0.63 < 0.633$

Mar 5, 2018

$0.06 \text{ "0.6" "0.603" "0.63" } 0.633$

#### Explanation:

Write them with the same number of decimal places as this makes them easier to compare.

Then write them underneath each other with the decimal points aligned. Then compare the place holders, working from left to right to identify the biggest and smallest numbers,

$0.630$
$0.600$
$0.633$
$0.603$
$0 \textcolor{b l u e}{.0} 60 \text{ } \leftarrow$ this is the smallest. There are $\frac{0}{10}$

All the others have at least $\frac{6}{10} \text{ } \left(0.6\right)$

Consider the second decimal places (hundredths)

$0.6 \textcolor{red}{3} 0 \text{ } \leftarrow$ bigger
$0.6 \textcolor{red}{0} 0 \text{ } \leftarrow$ smaller
$0.6 \textcolor{red}{3} 3 \text{ } \leftarrow$ bigger  0.6color(red)(0)3" "larr# smaller

Re-arrange them:

$0.6 \textcolor{red}{0} 0 \text{ } \leftarrow$ smaller
$0.6 \textcolor{red}{0} 3 \text{ } \leftarrow$ smaller

$0.6 \textcolor{red}{3} 0 \text{ } \leftarrow$ bigger
$0.6 \textcolor{red}{3} 3 \text{ } \leftarrow$ bigger

Now compare the third decimal places:

$0.60 \textcolor{\lim e g r e e n}{0} \text{ } \leftarrow$ smaller
$0.60 \textcolor{\lim e g r e e n}{3} \text{ } \leftarrow$ bigger

$0.63 \textcolor{red}{0} \text{ } \leftarrow$ smaller
$0.63 \textcolor{red}{3} \text{ } \leftarrow$ biggest of them all

The order from smallest to biggest is:

$0.06 \text{ "0.6" "0.603" "0.63" } 0.633$